segre(MultirationalMap) -- the composition of a multi-rational map with the Segre embedding of the target

i1 : ZZ/65521[x_0..x_4];

i2 : f = rationalMap({x_3^2-x_2*x_4,x_2*x_3-x_1*x_4,x_1*x_3-x_0*x_4,x_2^2-x_0*x_4,x_1*x_2-x_0*x_3,x_1^2-x_0*x_2},Dominant=>true);

o2 : RationalMap (quadratic dominant rational map from PP^4 to hypersurface in PP^5)

i3 : g = rationalMap {x_3^2-x_2*x_4,x_2*x_3-x_1*x_4,x_1*x_3-x_0*x_4,x_2^2-x_0*x_4,x_1*x_2-x_0*x_3};

o3 : RationalMap (quadratic rational map from PP^4 to PP^4)

i4 : h = rationalMap {-x_3^2+x_2*x_4,2*x_2*x_3-2*x_1*x_4,-3*x_2^2+2*x_1*x_3+x_0*x_4, 2*x_1*x_2-2*x_0*x_3,-x_1^2+x_0*x_2};

o4 : RationalMap (quadratic rational map from PP^4 to PP^4)

i5 : Phi = rationalMap {f,g,h};

o5 : MultirationalMap (rational map from PP^4 to hypersurface in PP^5 x PP^4 x PP^4)

i6 : time segre Phi;
 -- used 1.52494s (cpu); 1.12509s (thread); 0s (gc)

o6 : RationalMap (rational map from PP^4 to PP^149)

i7 : describe segre Phi

o7 = rational map defined by forms of degree 6
     source variety: PP^4
     target variety: PP^149
     coefficient ring: ZZ/65521